1/ The badges on the forum are just for fun I think, they show how active you are.
2/ It’s supposed to be the weapon you’re using, but it’s not. It usually shows a random weapon the game found pretty for you. It’s a small bug which really doesn’t matter anyway. Although some people seem really hung up about this for some reason.
3/ Yes but the devs have explained somewhere else that you might not be able to link the account with the console though.